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Chapter 18 | Electric Charge and Electric Field 801
where is the electrostatic force (or Coulomb force) exerted on a positive test charge . It is understood that is in the
same direction as . It is also assumed that is so small that it does not alter the charge distribution creating the electric field.
The units of electric field are newtons per coulomb (N/C). If the electric field is known, then the electrostatic force on any charge is simply obtained by multiplying charge times electric field, or . Consider the electric field due to a point charge .
According to Coulomb's law, the force it exerts on a test charge is . Thus the magnitude of the electric field, , for a point charge is
Since the test charge cancels, we see that
(18.12)
(18.13)
The electric field is thus seen to depend only on the charge and the distance ; it is completely independent of the test charge .
Example 18.2 Calculating the Electric Field of a Point Charge
Calculate the strength and direction of the electric field due to a point charge of 2.00 nC (nano-Coulombs) at a distance of 5.00 mm from the charge.
Strategy
We can find the electric field created by a point charge by using the equation .
Solution
Here C and m. Entering those values into the above equation gives
(18.14)
Discussion
This electric field strength is the same at any point 5.00 mm away from the charge that creates the field. It is positive, meaning that it has a direction pointing away from the charge .
Example 18.3 Calculating the Force Exerted on a Point Charge by an Electric Field
What force does the electric field found in the previous example exert on a point charge of ? Strategy
Since we know the electric field strength and the charge in the field, the force on that charge can be calculated using the definition of electric field rearranged to .
Solution
The magnitude of the force on a charge exerted by a field of strength N/C is thus,
(18.15)
Because is negative, the force is directed opposite to the direction of the field. Discussion
